Problem: The grades on a history midterm at Loyola are normally distributed with $\mu = 74$ and $\sigma = 3.0$. Daniel earned a n $81$ on the exam. Find the z-score for Daniel's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Daniel's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{81 - {74}}{{3.0}}} $ ${ z \approx 2.33}$ The z-score is $2.33$. In other words, Daniel's score was $2.33$ standard deviations above the mean.